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प्रश्न
What are the conditions for obtaining a good interference pattern? Give reasons.
What is the essential condition for obtaining sustained interference?
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उत्तर १
The conditions necessary for obtaining a well-defined and steady interference pattern are:
- The two sources of light should be coherent: This is the essential condition for getting a sustained interference pattern. As we have seen, the waves emitted by two coherent sources are always in phase or have a constant phase difference between them at all times. If the phases and phase differences vary with time, the positions of maxima and minima will also change with time, and the interference pattern will not be steady. For this reason, it is preferred that the two secondary sources used in the interference experiment are derived from a single original source.
- The light should be monochromatic: As can be seen from the condition of bright and dark fringes, the position of these fringes as well as the width of the fringes depend on the wavelength of light and the fringes of different colours are not coincident. The resultant pattern contains coloured, overlapping bands.
- The two interfering waves must have the same amplitude: Only if the amplitudes are equal, the intensity of dark fringes (destructive interference) is zero and the contrast between bright and dark fringes will be maximum.
- The two light sources should be narrow: If the slits are broad, the distances from different points along the slit to a given point on the screen are significantly different and therefore, the waves coming through the same slit will interfere among themselves, causing blurring of the interference pattern.
- The interfering light waves should be in the same state of polarization: Otherwise, the points where the waves meet in the opposite phase will not be completely dark and the interference pattern will not be distinct.
- The two waves should be in the same state of polarization: This is necessary only if polarized light is used for the experiment.
उत्तर २
- The two light sources must be coherent, which implies that the light waves they emit must have a constant phase difference or be the same phase.
- The two series must emit light of the same wavelength, but the amplitude between them should differ as little as possible.
संबंधित प्रश्न
A narrow slit S transmitting light of wavelength λ is placed a distance d above a large plane mirror, as shown in the following figure. The light coming directly from the slit and that coming after the reflection interfere at a screen ∑ placed at a distance D from the slit. (a) What will be the intensity at a point just above the mirror, i.e. just above O? (b) At what distance from O does the first maximum occur?
A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1.0 m away from the slit. If the mirror reflects only 64% of the light energy falling on it, what will be the ratio of the maximum to the minimum intensity in the interference pattern observed on the screen?
Answer in brief:
Explain what is the optical path length. How is it different from actual path length?
What are the two methods for obtaining coherent sources in the laboratory?
Two coherent sources whose intensity ratio is 25:1 produce interference fringes. Calculate the ratio of amplitudes of light waves coming from them.
Describe geometry of the Young’s double slit experiment with the help of a ray diagram. What is fringe width? Obtain an expression of it. Write the conditions for constructive as well as destructive interference.
In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to ______.
Obtain the relation between phase difference and path difference.
What is a bandwidth of interference pattern?
Two independent monochromatic sources cannot act as coherent sources, why?
The light waves from two independent monochromatic light sources are given by, y1 = 2 sin ωt and y2 = 3 cos ωt. Then the correct statement is ____________.
On a rainy day, a small oil film on water shows brilliant colours. This is due to ____________.
In Young's experiment for the interference of light, the separation between the silts is d and the distance of the screen from the slits is D. If D is increased by 0.6% and d is decreased by 0.2%, then for the light of a given wavelength, which one of the following is true?
"The fringe width ____________."
In a double slit experiment, the two slits are 2 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?
Two sources of light 0.5 mm apart are placed at a distance of 2.4 m and wavelength of light is 5000 Å. The phase difference between the two light waves interfering on the screen at a point at a distance 3 mm from central bright band is ____________.
In a biprism experiment, red light of wavelength 6500 Å was used. It was then replaced by green light of wavelength 5200 Å. The value of n for which (n + 1)th green bright band would coincide with nth red bright band for the same setting is ______.
In the Young's double slit experiment, if the phase difference between the two waves interfering at a point is `phi`, the intensity at that point is proportional to ____________.
If two waves represented by `"y"_1 = 3 "sin" omega "t"` and `"y"_2 = 5 "sin" (omega "t" + pi/3)` interfere at a point, then the amplitude of the resulting wave will be about ____________.
In a biprism experiment, monochromatic light of wavelength (λ) is used. The distance between two coherent sources is kept constant. If the distance between slit and eyepiece (D) is varied as D1, D2, D3, and D4, the corresponding measured fringe widths are z1, z2, z3, and z4 then ______
In the biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from dA to dB, then the fringe width is changed from ZA to ZB. The ratio ZA to ZB is ______
In Young's double-slit experiment, if the two sources of light are very wide, then ______.
In Young's double slit experiment, for wavelength λ1 the nth bright fringe is obtained at a point P on the screen. Keeping the same setting, source of light is replaced by wavelength λ2 and now (n + 1)th bright fringe is obtained at the same point P on the screen. The value of n is ______.
Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive 90° out of phase is ______.
`[cos pi/2=0]`
In an interference experiment, the intensity at a point is `(1/4)^"th"` of the maximum intensity. The angular position of this point is at ____________.
(cos 60° = 0.5, `lambda` = wavelength of light, d = slit width)
A beam of electrons is used in Young's double-slit experiment. If the speed of electrons is increased then the fringe width will ______.
How will the interference pattern of Young's double slit change if one of the two slits is covered by a paper which transmits only half of the light intensity?
